Lets here some ideas, i'm pretty open to anything honestly as long as it's understandable from a speaking perspective.
I absolutely love Helen Boksle, and I have been listening to her music since 2009, even though I never studied Norwegian, I just absolutely love world music. She has beautiful music, check this one out. Such a strong and melodic voice. Also I think this song is patriotic of some sort.
I'm a fan of Kaizers Orchestra, Razika, Siri Nilsen and Silja Sol personally :) but I'm discovering new (to me) artists all the time!
Kaizers are excellent but from a speaking point of view.... Unless you're specialising in Stavanger dialect! Their music is really good though. Another artist who I love but she sings in full Bergensk is Gabrielle Leithaug, bit of everything with her but I love what she does. (And yes Q I'm gonna comment on everything you post :D)
Collection of a lot of norwegian music. (Pop/Rock, christmas, children, funny songs and so on.)